Practice More Questions From: Assessment: Jacobians and Hessians

## Q:

### In this assessment, you will be tested on all of the different topics you have in covered this module. Good luck! Calculate the Jacobian of the function f(x,y,z)=x2cos(y)+ezsin(y)f(x, y, z) = x^2cos(y) + e^zsin(y)f(x,y,z)=x2cos(y)+ezsin(y) and evaluate at the point (x,y,z)=(π,π,1)(x, y, z) = (pi, pi, 1)(x,y,z)=(π,π,1).

## Q:

### Calculate the Jacobian of the vector valued functions: u(x,y)=x2y−cos(x)sin(y)u(x, y) = x^2y – cos(x)sin(y)u(x,y)=x2y−cos(x)sin(y) and v(x,y)=ex+yv(x, y) = e^{x+y}v(x,y)=ex+y and evaluate at the point (0,π)(0, pi)(0,π).

## Q:

### Calculate the Hessian for the function f(x,y)=x3cos(y)−xsin(y)f(x, y) = x^3cos(y) – xsin(y)f(x,y)=x3cos(y)−xsin(y).

## Q:

### Calculate the Hessian for the function f(x,y,z)=xy+sin(y)sin(z)+z3exf(x, y, z) = xy + sin(y)sin(z) + z^3e^xf(x,y,z)=xy+sin(y)sin(z)+z3ex.

## Q:

### Calculate the Hessian for the function f(x,y,z)=xycos(z)−sin(x)eyz3f(x, y, z) = xycos(z) – sin(x)e^yz^3f(x,y,z)=xycos(z)−sin(x)eyz3 and evaluate at the point (x,y,z)=(0,0,0)(x, y, z) = (0, 0, 0)(x,y,z)=(0,0,0)

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